Hotelling’s rule

What should the owner of a non-renewable resource do? Should they keep the commodity in the ground and hope for a better price next year, or should they extract it now and sell it to invest the proceeds in an interest bearing asset? Therein lies the fundamental decision underpinning one of the earliest theories around resource extraction, developed by American economist and statistician Harold Hotelling in 1931.

Hotelling’s rule (or Hotelling’s theory) states that the most profitable extraction path for a non-renewable resource is one along which the price of the commodity (determined by the marginal net revenue from its sale) increases at the prevailing rate of interest.

For example, if an oil producer believes that oil prices are unlikely to increase by more than the prevailing interest rate then they would be better off selling as much oil as possible and investing the proceeds in an interest bearing security such as US Treasuries. Conversely, if they expect crude prices to increase at a faster rate than the prevailing interest rate then the producer would be better off keeping the oil in the ground and waiting for a higher price.

All else being equal Hotelling’s rule implies that a rise in interest rates will increase the incentive for oil producers to hike output – they can park the proceeds and earn the yield. However, higher supply should also depress oil prices. The opposite is implied by the rule in the event that interest rates decline.

Given the existence of positive real interest rates, Hotelling’s rule predicts that the price of energy and other commodities should gradually increase over time. However, that’s not what the evidence shows though. Rather than increasing in price over time, commodity prices have typically remained stable in real terms – although oil prices are a notable exception.

Like most models, Hotelling’s rule includes a number of simplifying assumptions which means it doesn’t accurately reflect the real world. For example, the simple Hotelling rule also assumes that the marginal cost of production is zero – the difference between it and the price is known as the Hotelling rent. This assumption means that the price of the extracted resource held in stock, and that of the resource still in the ground are equivalent and so Hotelling’s rule applies equally to both.

In the real world marginal extraction costs could increase as producers are forced to develop more extreme deposits (e.g. the deep ocean or the frozen Arctic), or they could also decline (e.g. technological innovation as seen during the US shale boom). In the case that marginal extraction costs increase over time the price of the resource should rise at a slower rate than implied by the discount interest rate, and vice versa. A decline in marginal extraction costs over time means that the price needs to rise at a faster rate than that implied by the discount interest rate.

Producers are likely to face both short and long term capacity constraints. Producers can only expand output so quickly in the short term without resulting in dramatically higher marginal extraction costs. While in the longer term the depletion of the resource reserve beyond a certain point may only be possible in the event of a jump in either prices or technology, or both.

The motivation to continue to produce may also be influenced by other strategic, or non-monetary factors. Not all producers are 100% profit maximisers. For example, producers may also consume the resource too (crude oil could be used to feed the producing country’s refineries), and so if they didn’t produce it they would need to import it from elsewhere. Commodity producers (especially energy) may also wield geopolitical power which means their production decisions are not simply limited to the price and the interest rate, but to other strategic leverage they have over their neighbours.

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